obtained at temperature T* and under pressure p * , and the value of Henry's constant K a n 8 Bunsen's solubility coefficient (absorption coefficient) CY can be calculated from the formulae
Data obtained from this investigation are compared to literature (4) in Table 111. CONCLUSIONS
The present method is valid for determining Van Slyke factors and for determining the amount of gas dissolved in a
liquid employing gas chromatography. This technique can be applied to a solution containing more than one gas if the gases in question can be resolved. Furthermore, the method described should be applicable for determining the partial pressure of components of some organicaqueous and some organic-organic systems. ACKNOWLEDGMENT
The author thanks Hermann J. Donnert, U. S. Army Nuclear Defense Laboratory, for the extensive critique and constructive suggestions; these efforts have substantially contributed to improve the presentation of this work.
LITERATURE CITED
(1) Adams, G. E., Anderson, A. R., Van
Slyke Factors for Hydrogen, Oxygen, Carbon Dioxide and Carbon Monoxide, ANL-5991 (1959'1. (2) Anderson; A. R., Hart, E. J., J . Phys. Chem. 6 6 , 70 (1962). ( 3 ) DOLIlas, E., Ibid., 68, 169 (1964). (4) H an book of Chemistry and Physics, 44th Ed.. DD. 1706-1709 Chem. Rubber Co., Clevdand, Ohio, 1961. (5) Ramsey, J. H., Sczence 129, 900
3
(19.59). \----, (6) \'an Slyke, D. D., Harington, C. It., J . Bid. Chem. 61, 575 (1924). (7) Van Slyke, D. I)., Neill, J. M., Ibid., p. 523. (8)Van Slvke. D. D.. Stadie. W. C.. ' Zbid., 49,"l (1921). ' RONALD A. SASE
U. S. Army Yuclear Defense Laboratory Edgewood Arsenal, Md.
Polarographic Reduction of Tin(lV) in the Presence of 3-Mercaptopropionic Acid SIR: The polarographic analysis of tin(1V) is ordinarily carried out in chloride (3) or pyrogallol supporting electrolytes (6). I n both solutions, the acidity must be closely controlled within rather narrow limits to obtain wellformed polarographic waves. I n addition, polarograms of the tin (1V)-pyrogallol chelate show a dip in the limiting" current at negative potentials which could be a complicating factor in simultaneous analyses (6). I n this respect, tin(1V) is readily reduced from perchlorate, tartrate, citrate, and ammoniacal solutions in the presence of 3-mercaptopropionic acid. The polarographic waves are well formed and appear suitable for analytical applications in the supporting electrolytes investigated. I n addition, the acidity in perchlorate solution may be varied over a rather wide range, and the polarograms do not show a limiting current dip.
3.40 seconds, the flow rate was 4.34 mg./ second. Chemicals. All inorganic chemicals were of reagent grade. T h e stock tin(1V) solution was prepared from sodium stannate dihydrate (J. T. Baker Co.) by dissolving t h e solid material in 0.1M sodium hydroxide solution. 3-Mercaptopropionic acid (Matheson Coleman & Bell or Evans Chemetics material) was used as received. Procedure. A known volume of supporting electrolyte was deaerated by nitrogen bubbling. Sufficient 3mercaptopropionic acid was added so t h a t t h e final solution concentration was 0 . 2 M , then the tin(1V) aliquot
RESULTS A N D DISCUSSION
EXPERIMENTAL
Apparatus. All polarograms were recorded o n a Sargent Model XXI instrument. T h e saturated calomel electrode contained a flowing junction which served to separate the solution under investigation from the reference electrode ( 1 ) . The flowing junct;on was filled with 0.1M sodium nitrate when perchlorate was the supporting electrolyte. The temperature was maintained at 25' C. by means of a thermostated water bath. T o minimize convection effects caused by vibrations, the water bath containing the cell and electrode assembly was placed on a heavy slab. The slab was then placed on a rubber inner tube, which served as a shock mount. The drop-time was
was added. This sequence of addition was followed to minimize possible air oxidation of the mercaptan and to avoid hydrolysis of the tin(1V). When tin(1V) was added before the mercaptic acid in perchlorate solutions, a temporary opalescence-caused by formation of hydrolytic tin(1V)-was sometimes observed. Hydrolysis was even more marked in the ammonia buffer solution under these conditions. After the nitrogen bubbling step, polarograms were obtained in the usual manner. Addition of 3-mercaptopropionic acid to the 2M ammonia buffer so that the final concentration of complexing agent was 0.2M caused the p H to change from 9.5 to 9.3. For the more acidic solutions, the p H was not decreased significantly on adding a comparable amount of the mercaptic acid.
-0 2
-06 VOLTS
-1
0
SCE
Figure 1. Polarogram of tin(lV) in presence of 3-mercaptopropionic acid A.
B.
0.1 M Perchloric acid, p H = 1.0 0.1M Perchloric acid, p H = 1.0, 0.2M 3-mercaptopropionic acid, 2.00 X 10-4M tin(1VI
The polarographic reduction of the tin(IV)-3-mercaptopropionic acid complex was investigated in perchlorate, citrate, tartrate, ammoniacal, phosphate, and sodium hydroxide supporting electrolytes. Ordinarily, polarographic reduction of tin(1V) in these solutions produces kinetically hindered waves with limiting currents considerably less than predicted for solutions of these concentrations (3). However, in the presence of 3-mercaptopropionic acid, the usual two reduction waves for tin(1V) mere obtained in all supporting electrolytes except the last two. Typical polarographic waves are shown for supporting electrolytes composed of 0.1M perchloric acid (Figure 1, curve B ) , 0.1.11 tartaric acid (Figure 2, curve C), and 2M ammonium hydroxide, 21M ammonium chloride buffer (Figure VOL. 3 7 , N O . 4, APRIL 1965
607
16
12
vi
t 5-
vi
ai
8
W LL
I-.
8
u 3
6
a 0
0 -0 8
-0 4
VOLTS vs
Figure 2 .
0
-1.2
I
SC E
Polarograms of tin(lV) in
0.1N
I
II
I -0 8
tartaric acid
I
1
-I 2
VOLTS vs
0.1 M Tartaric acid, p H = 2.0, 1 .OO X IO-% Sn(lV) 6. 0.1M Tartaric acid, p H = 2.0, 1.00 X I0-W Sn(iV1. 0.2M Pyrogalla1 C. 0.1M Tartaric acid, p H = 2.0, 1.00 X IO-% Sn(lV). 0.2M 3 - M e r captopropionic acid
A.
I
1 -I 6
SCE
Figure 3. Polarogram of tin(lV) in 2M ammonium hydroxide, 2M ammonium chloride A. 6.
2M Ammonium hydroxide, 2M ammonium chloride, p H = 9.5 2M Ammonium hydroxide, 2M ammonlum chlorlde. 0.2M 3-mercaptopropionic acid
C. 2M Ammonium
hydroxide, 2M ammonium chloride, 0.2M 3-mercaptopropionic acld, 0.005% gelatin, 1 .OO X 1 OC3MSn(lV)
Table I.
Limiting Current as a Function
of Tin(lV) Concentration
(Supporting electrolyte: 0.1M perchloric acid or as noted) Tin(1V) concn., C, moles/ liter 2.00 x 4.00 x 5.00 x 6.00 X 8.00 x 1.00 x 5.00 x 5.00 x 5.00 x 5.00 X 1.00 x 1.25 x 5.00 X
Limiting current, i d ] Ira.
10-4 10-4 10-4
id/Cz
pa./ mmoles/ liter
3.00 6.26 7.43 9.42 12.5 15.6 7.43 7.45 7.54 6.49 13.3 16.6 6.55
10-4 10-3 10-4" 10-4b 10-4c 1010-3d 14-4c
15.0 15.6 14.9 15.7 15.6 15.6 14.9 150 15.1 13.0 13.3 13.3 13.1
1M Perchloric acid. 0.1M Ammonium perchlorate, pH = 2.0. c 0.1M Ammonium Derchlorate,. .pH = 3.0. d 0.1M Tartaric acid, pH = 2.0. 0.1M Citric acid, pH = 2.2. Q
b
Table II.
Limiting Current as a Function
of Tin(lV) Concentration
QSupporting electrolyte: 2M ammonium chloride, 2 M ammonium hydroxide, pH 9.3)
Tin(1V) concn., C, mole/ liter 2.00 x 4.00 x 5.00 x 6.00 X 8.00 X 1.00 x
608
10-4 10-4 l0F
lo-'
id/c,
Limiting current ad,
Ira.
2.72 5.34 6.70 7.91 10.7 13.3, 13.7
Ira. / mmoles/ liter 13.6 13.3 13.4 13.2 13.4 13.3, 1 3 . 7
ANALYTICAL CHEMISTRY
3, curve C). As seen, the expected two reduction waves are obtained in each solution. The second wave in the 2M ammonia buffer solution, corresponding to reduction of tin(I1) to tin(amalgam), shows a maximum which is suppressed by a trace of gelatin. The current increase a t the more negative potentials in this solution is due to reduction of uncomplexed 3-mercaptopropionate ( 4 ) I n the presence of gelatin, reduction of the excess complexing agent appears to be inhibited, since the current rise is smaller under these conditions. The limiting current corresponding to the four electron reduction of tin(1V) to tin(ama1gam) in 0.1M perchloric acid increases linearly with increasing tin (IV) concentration, as shown in Table I. T o test the effect of changes in acidity, a series of experiments was run in which the perchloric acid concentration was varied from 0.001M to 1-M. As seen in Table I, the limiting current is essentially constant over the entire range of acid concentrations. This contrasts with the pyrogallol-tin(1V) chelate in perchlorate solutions, where the limiting current decreases as the acidity is decreased (2, 6). I n tartrate and citrate solutions, the limiting currents are somewhat smaller than in perchlorate solutions, possibly reflecting a decreased diffusion coefficient, caused by complexation of the mercaptopropionate complex with the supporting electrolyte. The variation in limiting current with tin(1V) concentration was also investigated in 2.M ammonia buffer (pH 9.3). As shown in Table 11, this relationship is linear over the concentraI
tion range studied. When the p H was raised to 10.4 by addition of excess ammonium hydroxide, the limiting current decreased by about 20%, while a t pH 11, the two reduction waves were less than half the values a t pH 9.3. Evidently, significant amounts of stannate ion are formed a t the higher pH values, and stannate ion does not form a complex with the 3-mercaptopropionate. In support of this, an electroreducible complex did not form in 0.1-1.M sodium hydroxide solutions, where the predominent tin(1V) species is stannate ion. Mercury(I1) is strongly complexed by sulfhydryl groups and shows an anodic wave due to dissolution of the mercury electrode ( 4 ) . This large anoyic wave masks the foot of the first tin(1V) reduction wave in all the solutions investigated so that logarithmic analysis of the rising portion was not attempted. This anodic wave extends under the first tin(1V) reduction wave (see Figure 3), with the result that most of the first wave is really the algebraic sum of a cathodic and anodic current. For thi! reason, the first wave appears smaller than expected. For comparative purposes, polarograms of tin(1V) were obtained in tartrate solution using pyrogallol and 3-mercaptopropionic acid as complexing agents. When excess pyrogallol was added to a solution of tin(1V) in 0.1X tartaric acid, a smaller limiting current was obtained than for an equal molar excess of 3-mercaptopropionic acid, as shown in Figure 2. Part of this difference could be due to a smaller diffusion cbefficient for the tin(1V)-pyro-
gallol chelate, but this difference may also be partially due to a kinetic complication, such as a preceding chemical reaction. The slight hump in Figure 2, curve -1, is caused by reduction of the tin(1V)-tartrate complex which shows a pronounced dip in the limiting current.
LITERATURE CITED
(1) Alberts,
1895 (1963). (2) Bard A J. Zbid 34 266 (1962). ( 3 ) Koltioff; M,: ~ i J . J.,~ “Polarography,” p. 526, Interscience, CHEM.
(6) Phillips, S. L., Morgan, E., ANAL.
G. S., Shain, I., ANAL.
‘lg2(lg61).
33y
359
New Yorkj 1952. (4) Ibid., p. 782. ( 5 ) Phillips, S. L., Ph.D. Thesis, Univ. of Wisconsin, Madison, Wis., 1964.
~
~
S.L.PHILLIPS R.~ A. TOOMEY ,
~
Data Systems Laboratory Dept. C27, Bldg. 702 International Business Machines Corp. Poughkeepsie, N. Y.
Evidence on the Effect of Column-to-Particle Diameter Ratio in Gas Chromatography SIR: Recently Sternberg and Poulson (3) pointed out that columns with a small column-to-particle diameter ratio, d,/d,, perform unusually well because of reduced plate, H , and reduced pressure drop. Earlier Giddings (1) speculated, follouing the then surprising observation ( 2 ) of H < d, for dJd, -4, that the small plate height might be due to the effective shortening of the diffusion distance between points of unequal flow. We wish to test and discuss this hypothesis, insofar as possible, in the light of Sternberg and Poulson’s experimental results. THEORY
Each velocity inequality between two neighboring points (or regions) of a column will create a degree of nonequilibrium and thus contribute to plate height. Other things being equal the contribution will increase with the square of the diffusion distance (the distance between the two points). This is assuming that the velocity is not too high so that the relevant term, C,, has not yet been rendered negligible by coupling. Although in a random packing the extremes of the flow inequalities will be varying distances apart, it is likely that we can approximate the main effect by a single characteristic length, 1. Assuming that the principal effect arises from particle bridging (the so-called short range interchannel effect) we expect 1 to be 1.25 d, or thereabouts ( 1 ) . In Figure 1 we show in schematic fashion points of unusually high velocity (+ sign) and unusually low velocity
WALL
Figure 1. Regions with strong nonequilibrium polarization and their intersection by column wall
(- sign). In effect these neighboring points form nonequilibrium “dipoles” covering roughly the elliptical regions shown between the points. Some of these nonequilibrium “dipoles” would be cut in two if a small diameter column were somehow inserted into the chromatographic medium without disturbing it. The nonequilibrium effect would thus be reduced since some of these “dipoles” would exist only in part, and contribute less to plate height. For the sake of simplicity it will be assumed that the “dipoles” are randomly placed and that each one is weighted in effect by the length remaining within the circle (representing the column cross section). Thus the “average” length, assuming as above that one length characterizes the nonequilibrium, is i = 2 lL2/21t.The C, or w term (where C, = wdP2/D,) is thus reduced in small columns in proportion to i2/12. (If one did not use a single length to characterize nonequilibrium, a slightly better result might be gotten from i2 = Z , 3 / E l , . ) The results of this paper are calculated, therefore, on the assumption that W / W , = i2/12,where w and W, are the coefficients corresponding to the effect under discussion, with w, applying to a column approaching infinity in diameter. CALCULATIONS
The average length, i, remaining within the column cross section can be obtained in several ways. The problem can be set up in a straight-forward way by geometric arguments, but the result is a double integration involving an elliptical integral. A nonanalytical approach consists of drawing out a circle and letting sticks of a given length fall in its neighborhood; the average length of stick within the circle can then be identified with 2. Our approach was somewhere beta een the two in which the calculational problems were easily handled by computer. I n effect the computer averages the “stick” length by placing the center of the “stick” successively in 100 radial positions (properly weighted), and then rotating it through 200 angular positions. This
program could undoubtedly be streamlined, but there was no need for this since it was no particular burden to the I B M 7040. Each of the 20,000 such numbers, which are then averaged (after weighting), is obtained by simple trigonometric equations. There is no restriction on column diameter in these calculations other than the obvious one, d,/d, > 1. The value of d, can be larger or smaller than 1. RESULTS
Figure 2 shows a plot of W/W, (= i2/ P) us. the particle-to-column diameter These results were calratio, d,/d,. culated by assuming l / d , values of 1.25 and 2.5, respectively. For comparison the results of Sternberg and Poulson are shown. The latter plots are rather arbitrary because W , cannot really be
-
CALC. RESULTS ---EXP, STERNBERG 8 POULSON
.9-
.0-
.7.6-
Y w- . 5 .4
-
.3-
04
0
.2
.4
.6
I
.8
1.0
dJd, Figure 2. Comparison of experimental and theoretical values of relative w term, w / w , VOL. 37, NO. 4, APRIL 1965
e
609
